Suppose that X and Y are jointly continuous with joint probability density function fX, Y px, yq " # xe´xp1`yq if x ą 0 and y ą 0, 0 otherwise. (a) Find the marginal density functions of X and Y . (b) Calculate the expectation ErXY s (c) Find the conditional density function of X given Y " y.

A, b, c, and d have the coordinates (-8, 1), (-2, 4), (-3, -1), and (-6, 5), respectively. which sentence about the points is true? a. a, b, c, and d lie on the same line. b. and are perpendicular lines. c. and are parallel lines. d. and are intersecting lines but are not perpendicular. e. and are parallel lines.

Match the vocabulary to the proper definition. in probability, two events in which 1. conditional probability the outcome of one event is independent of the outcome of a second event. 2. dependent events in probability, two events in which the outcome of one event is dependent on the outcome of a second event. the probability of an event in which the outcome of the event is conditional on the outcome of one or more different events. 3. independent events

The length of an intercepted arc of a central angle of a circle is 4 cm. if the radius of the circle is 5 cm what is the measurement of the central angle to the nearest whole degree